// *****************************************************************************
// Copyright (c) 2005 - 2017 Qualcomm Technologies International, Ltd.
// %%version
//
// *****************************************************************************

#ifndef FFT_TWIDDLE_INCLUDED
#define FFT_TWIDDLE_INCLUDED

// On 24-bit Kalimba, when FFT_LOW_RAM is defined
// twiddle factors must be packed into 16-bit windowed flash
#define FFT_TWIDDLE_PACKED24    (defined(FFT_LOW_RAM) && !defined(K32))

// On 32-bit Kalimba, when FFT_LOW_RAM is defined
// twiddle factors should be placed in CONST
#if defined(FFT_LOW_RAM) && defined(K32)
   #define DM_REAL_TWIDDLE   CONST
   #define DM_IMAG_TWIDDLE   CONST
#endif

.MODULE $M.fft_twiddle;
   .DATASEGMENT DM;

   #if defined(FFT_LOW_RAM) // In this variant, fft twiddle factors are stored externally ...
      .VAR $fft.twiddle_real_address;      // and the pointers are loaded in  ...
      .VAR $fft.twiddle_imag_address;      // these variables.
      .CONST $FFT_LOW_RAM_USED       1;
   #else
      .CONST $FFT_LOW_RAM_USED       0;
   #endif

   #if defined(FFT_TWIDDLE_NEED_2048_POINT)

      .CONST   $fft.NUM_POINTS   2048;

      // twiddle factors needed for <= 2048 point fft and ifft routines
      #if FFT_TWIDDLE_PACKED24
         .VAR/DMCONST_WINDOWED16 $fft.twiddle_real[] =
            0x7FFF,  0xFF00,  0x0000,  0x5A82,  0x7AA5,  0x7D86,  0x7641,  0xAFCF,  0x043B,  0x30FB,  0xC589,  0xBE51,
            0x7D8A,  0x5FE7,  0x0748,  0x471C,  0xED95,  0x9267,  0x6A6D,  0x99B8,  0xE313,  0x18F8,  0xB882,  0x75A1,
            0x7F62,  0x37F3,  0x742D,  0x5133,  0xCD9D,  0x0DFE,  0x70E2,  0xCCC3,  0xA946,  0x2528,  0x0C85,  0x82FB,
            0x7A7D,  0x05DA,  0xD7F4,  0x3C56,  0xBA8F,  0x1D34,  0x62F2,  0x02AE,  0xCC33,  0x0C8B,  0xD380,  0x9DC9,
            0x7FD8,  0x88F9,  0xB827,  0x55F5,  0xA5A1,  0x2883,  0x73B5,  0xECC9,  0x45E0,  0x2B1F,  0x3587,  0x7B7C,
            0x7C29,  0xFCE0,  0xE607,  0x41CE,  0x1E92,  0x35F3,  0x66CF,  0x81B3,  0xC020,  0x12C8,  0x1081,  0x62AA,
            0x7E9D,  0x56ED,  0x37F0,  0x4C3F,  0xE099,  0x307F,  0x6DCA,  0x0DBE,  0x31E2,  0x1F19,  0xF983,  0xD604,
            0x7884,  0x84D4,  0xE0CB,  0x36BA,  0x208C,  0x4A14,  0x5ED7,  0x7DAA,  0x0A5B,  0x0647,  0xD980,  0x2778,
            0x7FF6,  0x22FC,  0xDBD5,  0x5842,  0xDDA3,  0x4BDF,  0x7504,  0xD3CC,  0x210D,  0x2E11,  0x0A88,  0x93B1,
            0x7CE3,  0xCFE3,  0xF47E,  0x447A,  0xCD93,  0xDBD7,  0x68A6,  0x9FB6,  0x4BEB,  0x15E2,  0x1481,  0xE26C,
            0x7F09,  0x92F0,  0x54D9,  0x4EBF,  0xE99B,  0x1777,  0x6F5F,  0x03C0,  0xE8B6,  0x2223,  0xA584,  0xA2FC,
            0x798A,  0x24D7,  0xD947,  0x398C,  0xDD8D,  0xAAD3,  0x60EC,  0x38AC,  0x64D5,  0x096A,  0x9080,  0x58C9,
            0x7FA7,  0x37F6,  0x9570,  0x539B,  0x2B9F,  0x13C8,  0x7255,  0x2DC6,  0x7323,  0x2826,  0xB986,  0x75DC,
            0x7B5D,  0x04DD,  0xDC5B,  0x3F17,  0x4A90,  0xA0FD,  0x64E8,  0x89B1,  0x4017,  0x0FAB,  0x2780,  0xF66E,
            0x7E1D,  0x94EA,  0x1DEC,  0x49B4,  0x1597,  0x5961,  0x6C24,  0x29BB,  0x8533,  0x1C0B,  0x8283,  0x1C31,
            0x776C,  0x4FD1,  0xEEF6,  0x33DE,  0xF38A,  0xFB2D,  0x5CB4,  0x21A7,  0xBD23,  0x0324,  0x2B80,  0x09DE,
            0x7FFD,  0x88FE,  0x6DE3,  0x5964,  0x65A4,  0x62EF,  0x75A5,  0x86CD,  0x91AB,  0x2F87,  0x5289,  0x26B6,
            0x7D39,  0x81E5,  0x7D60,  0x45CD,  0x3694,  0xB50E,  0x698C,  0x24B7,  0x961A,  0x176D,  0xDA82,  0x2999,
            0x7F38,  0x58F1,  0xE43D,  0x4FFB,  0x659C,  0x10CD,  0x7023,  0x11C2,  0x47CD,  0x23A6,  0x8885,  0x109D,
            0x7A05,  0xEFD9,  0x57DE,  0x3AF2,  0xEF8E,  0x61D3,  0x61F1,  0x00AD,  0x96EE,  0x0AFB,  0x6880,  0x78D4,
            0x7FC2,  0x56F8,  0x26A4,  0x54CA,  0x0AA0,  0x1C4C,  0x7307,  0xC4C7,  0xDB6C,  0x29A3,  0xC586,  0xF657,
            0x7BC5,  0xE3DF,  0x6090,  0x4073,  0xF291,  0x6956,  0x65DD,  0xFCB2,  0x7E9D,  0x1139,  0xF181,  0x2A1A,
            0x7E5F,  0xE5EB,  0xAA89,  0x4AFB,  0x6D98,  0x42F0,  0x6CF9,  0x35BC,  0xDA3F,  0x1D93,  0x5083,  0x76B4,
            0x77FA,  0xBAD3,  0x6704,  0x354D,  0x908B,  0xA062,  0x5DC7,  0x9DA8,  0xE211,  0x04B6,  0x1980,  0x1634,
            0x7FE9,  0xCCFB,  0x49E7,  0x571D,  0xEFA2,  0x3863,  0x745F,  0x9ECA,  0xB270,  0x2C98,  0xFC88,  0x0546,
            0x7C89,  0x4CE2,  0x6CB0,  0x4325,  0xC193,  0x06CB,  0x67BD,  0x10B5,  0x0493,  0x1455,  0x7781,  0xA01B,
            0x7ED5,  0xE6EE,  0xC60F,  0x4D81,  0x639A,  0x2204,  0x6E96,  0xAABF,  0x8C0E,  0x209F,  0x7084,  0x3A1D,
            0x7909,  0xA9D6,  0x5C3B,  0x3824,  0x948C,  0xF83C,  0x5FE3,  0xB4AB,  0x35F6,  0x07D9,  0x5C80,  0x3DAA,
            0x7F87,  0x2CF5,  0x0498,  0x5269,  0x129E,  0x0F00,  0x719E,  0x2DC5,  0x0D11,  0x26A8,  0x2285,  0xFA11,
            0x7AEF,  0x63DC,  0x5978,  0x3DB8,  0x338F,  0xDCEF,  0x63EF,  0x33B0,  0x049B,  0x0E1B,  0xC380,  0xC7A8,
            0x7DD6,  0x67E8,  0x9226,  0x4869,  0xE696,  0x73DC,  0x6B4A,  0xF2BA,  0x32CA,  0x1A82,  0xA082,  0xC67F,
            0x76D9,  0x4AD0,  0x78AE,  0x326E,  0x558A,  0x5A7A,  0x5B9D,  0x11A6,  0x9B9B,  0x0192,  0x1D80,  0x0278,
            0x7FFF,  0x62FF,  0x36F0,  0x59F3,  0xDEA4,  0xEFCA,  0x75F4,  0x2CCE,  0x4AB6,  0x3041,  0xC789,  0x71F1,
            0x7D62,  0x8BE6,  0x4234,  0x4675,  0x6895,  0x2337,  0x69FD,  0x61B8,  0x3C3E,  0x1833,  0x6782,  0x4F02,
            0x7F4D,  0xE4F2,  0xAC24,  0x5097,  0xFC9C,  0x8EEB,  0x7083,  0x79C2,  0xF83E,  0x2467,  0x7785,  0x4934,
            0x7A42,  0x11DA,  0x17BA,  0x3BA5,  0x1E8E,  0xBEF8,  0x6271,  0xFAAE,  0x312C,  0x0BC3,  0xAC80,  0x8AB2,
            0x7FCE,  0x0CF8,  0xEF5D,  0x5560,  0x41A0,  0xA1F2,  0x735F,  0x66C8,  0x9062,  0x2A61,  0xB187,  0x3854,
            0x7BF8,  0x88E0,  0x2324,  0x4121,  0x5991,  0xCF1D,  0x6657,  0x3DB3,  0x1F00,  0x1201,  0x1781,  0x45C6,
            0x7E7F,  0x39EC,  0x7124,  0x4B9E,  0x0498,  0xB938,  0x6D62,  0x28BD,  0x85BE,  0x1E56,  0xCA83,  0xA5C3,
            0x7840,  0x33D4,  0x23B2,  0x3604,  0x1B8B,  0xF4AC,  0x5E50,  0x01A9,  0x75CB,  0x057F,  0x0080,  0x1E39,
            0x7FF0,  0x94FC,  0x12D9,  0x57B0,  0xD2A2,  0xC1AE,  0x74B2,  0xC9CB,  0x697E,  0x2D55,  0x3B88,  0x4BE8,
            0x7CB7,  0x27E3,  0x3073,  0x43D0,  0x9B93,  0x70CB,  0x6832,  0x58B5,  0xA7E3,  0x151B,  0xE081,  0xC0A8,
            0x7EF0,  0x58EF,  0x8D60,  0x4E21,  0x069A,  0x9C40,  0x6EFB,  0x5FC0,  0x3A13,  0x2161,  0xB484,  0x6DF4,
            0x794A,  0x7CD7,  0x1A8F,  0x38D8,  0xFF8D,  0x50FA,  0x6068,  0x6DAB,  0xCCFE,  0x08A2,  0x0180,  0x4A9C,
            0x7F97,  0xCFF5,  0xCCF7,  0x5302,  0x859E,  0x90EC,  0x71FA,  0x39C5,  0xBFD2,  0x2767,  0x9E86,  0x3761,
            0x7B26,  0xCBDD,  0x1ABE,  0x3E68,  0x0B90,  0x3E6C,  0x646C,  0x5AB0,  0xA1F7,  0x0EE3,  0x8780,  0xDE6E,
            0x7DFA,  0x99E9,  0x57ED,  0x490F,  0x5896,  0xE61D,  0x6BB8,  0x13BA,  0xDBA9,  0x1B47,  0x3382,  0xF0BE,
            0x7723,  0x5FD1,  0x3398,  0x3326,  0xE38A,  0xAA43,  0x5C29,  0x0BA7,  0x2BF1,  0x025B,  0x2780,  0x058D,
            0x7FFA,  0x73FD,  0xA4D9,  0x58D4,  0x0FA3,  0xD6F5,  0x7555,  0xBDCC,  0xD91D,  0x2ECC,  0x6888,  0xDCA1,
            0x7D0F,  0x42E4,  0xB8CD,  0x4524,  0x5794,  0x47ED,  0x6919,  0xE3B6,  0xF0A8,  0x16A8,  0x1382,  0x0567,
            0x7F21,  0x92F1,  0x1C79,  0x4F5E,  0x099B,  0x93A6,  0x6FC1,  0x94C1,  0x97F5,  0x22E5,  0x4284,  0xD935,
            0x79C8,  0x9FD8,  0x9862,  0x3A40,  0x2E8E,  0x05C7,  0x616F,  0x14AC,  0xFD7B,  0x0A33,  0x0980,  0x6831,
            0x7FB5,  0x64F7,  0x5DFF,  0x5433,  0x029F,  0x9793,  0x72AF,  0x06C7,  0x2701,  0x28E5,  0x7186,  0xB584,
            0x7B92,  0x0CDE,  0x9E4C,  0x3FC5,  0xED91,  0x04A1,  0x6563,  0xC0B1,  0xDEFA,  0x1072,  0xA081,  0x0FA8,
            0x7E3F,  0x58EA,  0xE420,  0x4A58,  0x1D97,  0xCDA8,  0x6C8F,  0x35BC,  0x2F65,  0x1CCF,  0x8D83,  0x48D9,
            0x77B4,  0x18D2,  0xAAC5,  0x3496,  0x828B,  0x4D37,  0x5D3E,  0x52A8,  0x4F2E,  0x03ED,  0x2780,  0x0F6C,
            0x7FE1,  0xC7FA,  0x8100,  0x568A,  0x35A1,  0xAFFF,  0x740B,  0x54C9,  0xFBE5,  0x2BDC,  0x4E87,  0xBFCD,
            0x7C5A,  0x3DE1,  0xA936,  0x427A,  0x4292,  0x9DD8,  0x6746,  0xC8B4,  0x61FC,  0x138E,  0xDC81,  0x80C7,
            0x7EBA,  0x3AED,  0xFEE9,  0x4CE1,  0x0099,  0xA8C3,  0x6E30,  0xE3BE,  0xDEA7,  0x1FDC,  0xDC84,  0x0778,
            0x78C7,  0xACD5,  0x9E4F,  0x376F,  0x9E8C,  0xA09A,  0x5F5E,  0x0EAA,  0x9FBF,  0x0710,  0xA380,  0x31F4,
            0x7F75,  0x4EF4,  0x3C54,  0x51CE,  0xD49D,  0x8E06,  0x7141,  0x08C4,  0x5AE2,  0x25E8,  0x4685,  0xBDEF,
            0x7AB6,  0xCCDB,  0x9889,  0x3D07,  0xC28F,  0x7C87,  0x6371,  0x15AF,  0x6804,  0x0D53,  0xDC80,  0xB21C,
            0x7DB0,  0xFEE7,  0xCC99,  0x47C3,  0xC296,  0x029F,  0x6ADC,  0xC9B9,  0x8A98,  0x19BD,  0xCC82,  0x9D75,
            0x768E,  0x0FCF,  0xBE39,  0x31B5,  0x4A8A,  0x0BD4,  0x5B10,  0x36A6,  0x0C22,  0x00C9,  0x1080,  0x009E,
            0x7FFF,  0xD9FF,  0x9B78,  0x5A3B,  0x48A5,  0x368C,  0x761B,  0x12CE,  0xA769,  0x309E,  0xD589,  0x97FD,
            0x7D76,  0x9CE6,  0xA4B6,  0x46C9,  0x4095,  0x5AAE,  0x6A35,  0x9EB8,  0x8F92,  0x1896,  0x1782,  0x622B,
            0x7F58,  0x35F3,  0x1025,  0x50E5,  0xFD9C,  0xCE56,  0x70B3,  0x45C3,  0x50AF,  0x24C7,  0xCD85,  0x65F2,
            0x7A5F,  0xB1DA,  0x77CB,  0x3BFD,  0xFF8E,  0xEDF3,  0x62B2,  0x1CAE,  0x7E96,  0x0C27,  0xC480,  0x9416,
            0x7FD3,  0x71F9,  0x53C0,  0x55AB,  0x0DA0,  0xE51E,  0x738A,  0xCDC8,  0xEB10,  0x2AC0,  0x8087,  0x59C3,
            0x7C11,  0x68E0,  0x848B,  0x4177,  0xD092,  0x0266,  0x6693,  0x7FB3,  0x6F78,  0x1264,  0x9981,  0x5411,
            0x7E8E,  0x6FEC,  0xD484,  0x4BEF,  0x0998,  0xF4BC,  0x6D96,  0x3CBD,  0xDBBB,  0x1EB8,  0x6B83,  0xBDBD,
            0x7862,  0x81D4,  0x8231,  0x365F,  0x2E8C,  0x1F3C,  0x5E93,  0xDCA9,  0xBFF9,  0x05E3,  0x6F80,  0x22B1,
            0x7FF3,  0x82FC,  0x7756,  0x57F9,  0xF3A3,  0x06AA,  0x74DB,  0xF2CB,  0xC535,  0x2DB3,  0x3188,  0x6FA8,
            0x7CCD,  0xA1E3,  0x9270,  0x4425,  0xC993,  0xA62F,  0x686C,  0x9BB5,  0xF9D0,  0x157F,  0x0181,  0xD163,
            0x7EFD,  0x1CEF,  0xF117,  0x4E70,  0x909A,  0xD9BC,  0x6F2D,  0x53C0,  0x9151,  0x21C2,  0xB784,  0x8852,
            0x796A,  0x75D7,  0x79DE,  0x3933,  0x008D,  0x7DC4,  0x60AA,  0x70AC,  0x18CF,  0x0906,  0x4B80,  0x518B,
            0x7F9F,  0xAAF6,  0x3130,  0x534E,  0xF29E,  0xD23C,  0x7227,  0xD6C6,  0x1969,  0x27C7,  0x3886,  0x5679,
            0x7B42,  0x0DDD,  0x7B82,  0x3EBF,  0xBE90,  0x6F92,  0x64AA,  0x90B0,  0xF0EF,  0x0F47,  0x5C80,  0xEA47,
            0x7E0C,  0x3DE9,  0xBAE5,  0x4961,  0xCD97,  0x1F9F,  0x6BEE,  0x3FBB,  0x3059,  0x1BA9,  0x6383,  0x0651,
            0x7747,  0xFCD1,  0x9138,  0x3382,  0xFB8A,  0xD294,  0x5C6E,  0xB2A7,  0x746F,  0x02BF,  0xAA80,  0x078E,
            0x7FFC,  0x25FE,  0x095D,  0x591C,  0x55A4,  0x1CD6,  0x757D,  0xC6CD,  0x3555,  0x2F29,  0xEC89,  0x0187,
            0x7D24,  0x88E5,  0x1B0E,  0x4578,  0xDC94,  0x7E5C,  0x6953,  0x24B7,  0x434A,  0x170A,  0xFE82,  0x175A,
            0x7F2D,  0x1CF1,  0x8056,  0x4FAC,  0xD09B,  0xD21B,  0x6FF2,  0x75C1,  0xEFCE,  0x2345,  0xF084,  0xF4C3,
            0x79E7,  0x6DD8,  0xF814,  0x3A99,  0xA08E,  0x33AA,  0x61B0,  0x28AD,  0x4A1B,  0x0A97,  0x3C80,  0x705B,
            0x7FBC,  0x04F7,  0xC24F,  0x547E,  0xA09F,  0xD9D2,  0x72DB,  0x88C7,  0x8125,  0x2944,  0xA886,  0xD5C8,
            0x7BAC,  0x1DDE,  0xFF64,  0x401D,  0x0391,  0x36D9,  0x65A0,  0xFDB2,  0x2EB4,  0x10D6,  0x4E81,  0x1CBA,
            0x7E4F,  0xC5EB,  0x474F,  0x4AA9,  0xDC98,  0x082C,  0x6CC4,  0x57BC,  0x84BD,  0x1D31,  0x7783,  0x5FA0,
            0x77D7,  0x8ED3,  0x08D7,  0x34F2,  0x1A8B,  0x76A9,  0x5D83,  0x15A8,  0x9884,  0x0451,  0xA180,  0x12A8,
            0x7FE5,  0xF1FA,  0xE572,  0x56D4,  0x2DA1,  0xF414,  0x7435,  0x9DCA,  0x571A,  0x2C3A,  0xB387,  0xE265,
            0x7C71,  0xEBE2,  0x0AEA,  0x42D0,  0x1692,  0xD230,  0x6782,  0x0CB4,  0xB331,  0x13F2,  0x2F81,  0x904A,
            0x7EC8,  0x37EE,  0x6277,  0x4D31,  0x4999,  0xE544,  0x6E63,  0xE8BF,  0x3547,  0x203E,  0x3084,  0x20A4,
            0x78E8,  0xD0D5,  0xFD38,  0x37CA,  0x2A8C,  0xCC47,  0x5FA0,  0xFEAA,  0xEAC0,  0x0775,  0x0280,  0x37A8,
            0x7F7E,  0x65F4,  0xA072,  0x521C,  0x0D9D,  0xCE64,  0x716F,  0xBDC4,  0xB3E7,  0x2648,  0x3F85,  0xDBDB,
            0x7AD3,  0x3DDB,  0xF8F5,  0x3D60,  0x0D8F,  0xAC99,  0x63B0,  0x42AF,  0xB636,  0x0DB7,  0xD380,  0xBCBB,
            0x7DC3,  0xD9E8,  0x2F58,  0x4816,  0xEB96,  0x3B1D,  0x6B13,  0xFFB9,  0xDE9C,  0x1A20,  0x3E82,  0xB1D4,
            0x76B3,  0xD1D0,  0x1B64,  0x3211,  0xDF8A,  0x3303,  0x5B56,  0xC0A6,  0x53C3,  0x012D,  0x9780,  0x0163,
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      #else
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            -0.9997694054,
            -0.7221281939,
            -0.6917592584,
            -0.4024346509,
            -0.9154487161,
            -0.9318842656,
            -0.3627557244,
            -0.2161067971,
            -0.9763697313,
            -0.8432082396,
            -0.5375870763,
            -0.5732971667,
            -0.8193475201,
            -0.9847485018,
            -0.1739838734,
            -0.1193652148,
            -0.9928504145,
            -0.7864552136,
            -0.6176473079,
            -0.4902264833,
            -0.8715950867,
            -0.9629532669,
            -0.2696683256,
            -0.3107671527,
            -0.9504860739,
            -0.8918407094,
            -0.4523495872,
            -0.6508466850,
            -0.7592091890,
            -0.9970600703,
            -0.0766238614,
            -0.0705045734,
            -0.9975114561,
            -0.7552013769,
            -0.6554928530,
            -0.4468688402,
            -0.8945994856,
            -0.9485613499,
            -0.3165933756,
            -0.2637546790,
            -0.9645897933,
            -0.8685707060,
            -0.4955652618,
            -0.6128100824,
            -0.7902302214,
            -0.9920993131,
            -0.1254549834,
            -0.1679382950,
            -0.9857975092,
            -0.8158144108,
            -0.5783137964,
            -0.5324031279,
            -0.8464909388,
            -0.9750253451,
            -0.2220936210,
            -0.3570309612,
            -0.9340925504,
            -0.9129621904,
            -0.4080441629,
            -0.6873153409,
            -0.7263591551,
            -0.9996188225,
            -0.0276081458,
            -0.0460031821,
            -0.9989412932,
            -0.7388873245,
            -0.6738290004,
            -0.4247796812,
            -0.9052967593,
            -0.9405060706,
            -0.3397768844,
            -0.2400030224,
            -0.9707721407,
            -0.8561473284,
            -0.5167317990,
            -0.5932322950,
            -0.8050313311,
            -0.9887216920,
            -0.1497645347,
            -0.1436950332,
            -0.9896220175,
            -0.8013761717,
            -0.5981607070,
            -0.5114688504,
            -0.8593018184,
            -0.9692812354,
            -0.2459550503,
            -0.3339996514,
            -0.9425731976,
            -0.9026733182,
            -0.4303264813,
            -0.6692825883,
            -0.7430079521,
            -0.9986402182,
            -0.0521317047,
            -0.0949634953,
            -0.9954807555,
            -0.7710605243,
            -0.6367618612,
            -0.4686888220,
            -0.8833633387,
            -0.9560452513,
            -0.2932191627,
            -0.2873474595,
            -0.9578264130,
            -0.8804708891,
            -0.4741002147,
            -0.6320187359,
            -0.7749531066,
            -0.9948793308,
            -0.1010698628,
            -0.1920803970,
            -0.9813791933,
            -0.8297612338,
            -0.5581185312,
            -0.5530167056,
            -0.8331701647,
            -0.9801821360,
            -0.1980984107,
            -0.3798472089,
            -0.9250492408,
            -0.9227011283,
            -0.3855160538,
            -0.7049340804,
            -0.7092728264,
            -0.9999952938,
            -0.0030679568;
      #endif // FFT_LOW_RAM
   #else // FFT_TWIDDLE_NEED_2048_POINT
   #if defined(FFT_TWIDDLE_NEED_1024_POINT)

      .CONST   $fft.NUM_POINTS   1024;

      #if FFT_TWIDDLE_PACKED24
         .VAR/DMCONST_WINDOWED16 $fft.twiddle_real[] =
            0x7FFF,  0xFF00,  0x0000,  0x5A82,  0x7AA5,  0x7D86,  0x7641,  0xAFCF,  0x043B,  0x30FB,  0xC589,  0xBE51,
            0x7D8A,  0x5FE7,  0x0748,  0x471C,  0xED95,  0x9267,  0x6A6D,  0x99B8,  0xE313,  0x18F8,  0xB882,  0x75A1,
            0x7F62,  0x37F3,  0x742D,  0x5133,  0xCD9D,  0x0DFE,  0x70E2,  0xCCC3,  0xA946,  0x2528,  0x0C85,  0x82FB,
            0x7A7D,  0x05DA,  0xD7F4,  0x3C56,  0xBA8F,  0x1D34,  0x62F2,  0x02AE,  0xCC33,  0x0C8B,  0xD380,  0x9DC9,
            0x7FD8,  0x88F9,  0xB827,  0x55F5,  0xA5A1,  0x2883,  0x73B5,  0xECC9,  0x45E0,  0x2B1F,  0x3587,  0x7B7C,
            0x7C29,  0xFCE0,  0xE607,  0x41CE,  0x1E92,  0x35F3,  0x66CF,  0x81B3,  0xC020,  0x12C8,  0x1081,  0x62AA,
            0x7E9D,  0x56ED,  0x37F0,  0x4C3F,  0xE099,  0x307F,  0x6DCA,  0x0DBE,  0x31E2,  0x1F19,  0xF983,  0xD604,
            0x7884,  0x84D4,  0xE0CB,  0x36BA,  0x208C,  0x4A14,  0x5ED7,  0x7DAA,  0x0A5B,  0x0647,  0xD980,  0x2778,
            0x7FF6,  0x22FC,  0xDBD5,  0x5842,  0xDDA3,  0x4BDF,  0x7504,  0xD3CC,  0x210D,  0x2E11,  0x0A88,  0x93B1,
            0x7CE3,  0xCFE3,  0xF47E,  0x447A,  0xCD93,  0xDBD7,  0x68A6,  0x9FB6,  0x4BEB,  0x15E2,  0x1481,  0xE26C,
            0x7F09,  0x92F0,  0x54D9,  0x4EBF,  0xE99B,  0x1777,  0x6F5F,  0x03C0,  0xE8B6,  0x2223,  0xA584,  0xA2FC,
            0x798A,  0x24D7,  0xD947,  0x398C,  0xDD8D,  0xAAD3,  0x60EC,  0x38AC,  0x64D5,  0x096A,  0x9080,  0x58C9,
            0x7FA7,  0x37F6,  0x9570,  0x539B,  0x2B9F,  0x13C8,  0x7255,  0x2DC6,  0x7323,  0x2826,  0xB986,  0x75DC,
            0x7B5D,  0x04DD,  0xDC5B,  0x3F17,  0x4A90,  0xA0FD,  0x64E8,  0x89B1,  0x4017,  0x0FAB,  0x2780,  0xF66E,
            0x7E1D,  0x94EA,  0x1DEC,  0x49B4,  0x1597,  0x5961,  0x6C24,  0x29BB,  0x8533,  0x1C0B,  0x8283,  0x1C31,
            0x776C,  0x4FD1,  0xEEF6,  0x33DE,  0xF38A,  0xFB2D,  0x5CB4,  0x21A7,  0xBD23,  0x0324,  0x2B80,  0x09DE,
            0x7FFD,  0x88FE,  0x6DE3,  0x5964,  0x65A4,  0x62EF,  0x75A5,  0x86CD,  0x91AB,  0x2F87,  0x5289,  0x26B6,
            0x7D39,  0x81E5,  0x7D60,  0x45CD,  0x3694,  0xB50E,  0x698C,  0x24B7,  0x961A,  0x176D,  0xDA82,  0x2999,
            0x7F38,  0x58F1,  0xE43D,  0x4FFB,  0x659C,  0x10CD,  0x7023,  0x11C2,  0x47CD,  0x23A6,  0x8885,  0x109D,
            0x7A05,  0xEFD9,  0x57DE,  0x3AF2,  0xEF8E,  0x61D3,  0x61F1,  0x00AD,  0x96EE,  0x0AFB,  0x6880,  0x78D4,
            0x7FC2,  0x56F8,  0x26A4,  0x54CA,  0x0AA0,  0x1C4C,  0x7307,  0xC4C7,  0xDB6C,  0x29A3,  0xC586,  0xF657,
            0x7BC5,  0xE3DF,  0x6090,  0x4073,  0xF291,  0x6956,  0x65DD,  0xFCB2,  0x7E9D,  0x1139,  0xF181,  0x2A1A,
            0x7E5F,  0xE5EB,  0xAA89,  0x4AFB,  0x6D98,  0x42F0,  0x6CF9,  0x35BC,  0xDA3F,  0x1D93,  0x5083,  0x76B4,
            0x77FA,  0xBAD3,  0x6704,  0x354D,  0x908B,  0xA062,  0x5DC7,  0x9DA8,  0xE211,  0x04B6,  0x1980,  0x1634,
            0x7FE9,  0xCCFB,  0x49E7,  0x571D,  0xEFA2,  0x3863,  0x745F,  0x9ECA,  0xB270,  0x2C98,  0xFC88,  0x0546,
            0x7C89,  0x4CE2,  0x6CB0,  0x4325,  0xC193,  0x06CB,  0x67BD,  0x10B5,  0x0493,  0x1455,  0x7781,  0xA01B,
            0x7ED5,  0xE6EE,  0xC60F,  0x4D81,  0x639A,  0x2204,  0x6E96,  0xAABF,  0x8C0E,  0x209F,  0x7084,  0x3A1D,
            0x7909,  0xA9D6,  0x5C3B,  0x3824,  0x948C,  0xF83C,  0x5FE3,  0xB4AB,  0x35F6,  0x07D9,  0x5C80,  0x3DAA,
            0x7F87,  0x2CF5,  0x0498,  0x5269,  0x129E,  0x0F00,  0x719E,  0x2DC5,  0x0D11,  0x26A8,  0x2285,  0xFA11,
            0x7AEF,  0x63DC,  0x5978,  0x3DB8,  0x338F,  0xDCEF,  0x63EF,  0x33B0,  0x049B,  0x0E1B,  0xC380,  0xC7A8,
            0x7DD6,  0x67E8,  0x9226,  0x4869,  0xE696,  0x73DC,  0x6B4A,  0xF2BA,  0x32CA,  0x1A82,  0xA082,  0xC67F,
            0x76D9,  0x4AD0,  0x78AE,  0x326E,  0x558A,  0x5A7A,  0x5B9D,  0x11A6,  0x9B9B,  0x0192,  0x1D80,  0x0278,
            0x7FFF,  0x62FF,  0x36F0,  0x59F3,  0xDEA4,  0xEFCA,  0x75F4,  0x2CCE,  0x4AB6,  0x3041,  0xC789,  0x71F1,
            0x7D62,  0x8BE6,  0x4234,  0x4675,  0x6895,  0x2337,  0x69FD,  0x61B8,  0x3C3E,  0x1833,  0x6782,  0x4F02,
            0x7F4D,  0xE4F2,  0xAC24,  0x5097,  0xFC9C,  0x8EEB,  0x7083,  0x79C2,  0xF83E,  0x2467,  0x7785,  0x4934,
            0x7A42,  0x11DA,  0x17BA,  0x3BA5,  0x1E8E,  0xBEF8,  0x6271,  0xFAAE,  0x312C,  0x0BC3,  0xAC80,  0x8AB2,
            0x7FCE,  0x0CF8,  0xEF5D,  0x5560,  0x41A0,  0xA1F2,  0x735F,  0x66C8,  0x9062,  0x2A61,  0xB187,  0x3854,
            0x7BF8,  0x88E0,  0x2324,  0x4121,  0x5991,  0xCF1D,  0x6657,  0x3DB3,  0x1F00,  0x1201,  0x1781,  0x45C6,
            0x7E7F,  0x39EC,  0x7124,  0x4B9E,  0x0498,  0xB938,  0x6D62,  0x28BD,  0x85BE,  0x1E56,  0xCA83,  0xA5C3,
            0x7840,  0x33D4,  0x23B2,  0x3604,  0x1B8B,  0xF4AC,  0x5E50,  0x01A9,  0x75CB,  0x057F,  0x0080,  0x1E39,
            0x7FF0,  0x94FC,  0x12D9,  0x57B0,  0xD2A2,  0xC1AE,  0x74B2,  0xC9CB,  0x697E,  0x2D55,  0x3B88,  0x4BE8,
            0x7CB7,  0x27E3,  0x3073,  0x43D0,  0x9B93,  0x70CB,  0x6832,  0x58B5,  0xA7E3,  0x151B,  0xE081,  0xC0A8,
            0x7EF0,  0x58EF,  0x8D60,  0x4E21,  0x069A,  0x9C40,  0x6EFB,  0x5FC0,  0x3A13,  0x2161,  0xB484,  0x6DF4,
            0x794A,  0x7CD7,  0x1A8F,  0x38D8,  0xFF8D,  0x50FA,  0x6068,  0x6DAB,  0xCCFE,  0x08A2,  0x0180,  0x4A9C,
            0x7F97,  0xCFF5,  0xCCF7,  0x5302,  0x859E,  0x90EC,  0x71FA,  0x39C5,  0xBFD2,  0x2767,  0x9E86,  0x3761,
            0x7B26,  0xCBDD,  0x1ABE,  0x3E68,  0x0B90,  0x3E6C,  0x646C,  0x5AB0,  0xA1F7,  0x0EE3,  0x8780,  0xDE6E,
            0x7DFA,  0x99E9,  0x57ED,  0x490F,  0x5896,  0xE61D,  0x6BB8,  0x13BA,  0xDBA9,  0x1B47,  0x3382,  0xF0BE,
            0x7723,  0x5FD1,  0x3398,  0x3326,  0xE38A,  0xAA43,  0x5C29,  0x0BA7,  0x2BF1,  0x025B,  0x2780,  0x058D,
            0x7FFA,  0x73FD,  0xA4D9,  0x58D4,  0x0FA3,  0xD6F5,  0x7555,  0xBDCC,  0xD91D,  0x2ECC,  0x6888,  0xDCA1,
            0x7D0F,  0x42E4,  0xB8CD,  0x4524,  0x5794,  0x47ED,  0x6919,  0xE3B6,  0xF0A8,  0x16A8,  0x1382,  0x0567,
            0x7F21,  0x92F1,  0x1C79,  0x4F5E,  0x099B,  0x93A6,  0x6FC1,  0x94C1,  0x97F5,  0x22E5,  0x4284,  0xD935,
            0x79C8,  0x9FD8,  0x9862,  0x3A40,  0x2E8E,  0x05C7,  0x616F,  0x14AC,  0xFD7B,  0x0A33,  0x0980,  0x6831,
            0x7FB5,  0x64F7,  0x5DFF,  0x5433,  0x029F,  0x9793,  0x72AF,  0x06C7,  0x2701,  0x28E5,  0x7186,  0xB584,
            0x7B92,  0x0CDE,  0x9E4C,  0x3FC5,  0xED91,  0x04A1,  0x6563,  0xC0B1,  0xDEFA,  0x1072,  0xA081,  0x0FA8,
            0x7E3F,  0x58EA,  0xE420,  0x4A58,  0x1D97,  0xCDA8,  0x6C8F,  0x35BC,  0x2F65,  0x1CCF,  0x8D83,  0x48D9,
            0x77B4,  0x18D2,  0xAAC5,  0x3496,  0x828B,  0x4D37,  0x5D3E,  0x52A8,  0x4F2E,  0x03ED,  0x2780,  0x0F6C,
            0x7FE1,  0xC7FA,  0x8100,  0x568A,  0x35A1,  0xAFFF,  0x740B,  0x54C9,  0xFBE5,  0x2BDC,  0x4E87,  0xBFCD,
            0x7C5A,  0x3DE1,  0xA936,  0x427A,  0x4292,  0x9DD8,  0x6746,  0xC8B4,  0x61FC,  0x138E,  0xDC81,  0x80C7,
            0x7EBA,  0x3AED,  0xFEE9,  0x4CE1,  0x0099,  0xA8C3,  0x6E30,  0xE3BE,  0xDEA7,  0x1FDC,  0xDC84,  0x0778,
            0x78C7,  0xACD5,  0x9E4F,  0x376F,  0x9E8C,  0xA09A,  0x5F5E,  0x0EAA,  0x9FBF,  0x0710,  0xA380,  0x31F4,
            0x7F75,  0x4EF4,  0x3C54,  0x51CE,  0xD49D,  0x8E06,  0x7141,  0x08C4,  0x5AE2,  0x25E8,  0x4685,  0xBDEF,
            0x7AB6,  0xCCDB,  0x9889,  0x3D07,  0xC28F,  0x7C87,  0x6371,  0x15AF,  0x6804,  0x0D53,  0xDC80,  0xB21C,
            0x7DB0,  0xFEE7,  0xCC99,  0x47C3,  0xC296,  0x029F,  0x6ADC,  0xC9B9,  0x8A98,  0x19BD,  0xCC82,  0x9D75,
            0x768E,  0x0FCF,  0xBE39,  0x31B5,  0x4A8A,  0x0BD4,  0x5B10,  0x36A6,  0x0C22,  0x00C9,  0x1080,  0x009E;
      #else
         // twiddle factors needed for <= 1024 point fft and ifft routines
         .VAR/DM_REAL_TWIDDLE $fft.twiddle_real[512] =
            +1.0000000000,
            +0.0000000000,
            +0.7071067812,
            -0.7071067812,
            +0.9238795325,
            -0.3826834324,
            +0.3826834324,
            -0.9238795325,
            +0.9807852804,
            -0.1950903220,
            +0.5555702330,
            -0.8314696123,
            +0.8314696123,
            -0.5555702330,
            +0.1950903220,
            -0.9807852804,
            +0.9951847267,
            -0.0980171403,
            +0.6343932842,
            -0.7730104534,
            +0.8819212643,
            -0.4713967368,
            +0.2902846773,
            -0.9569403357,
            +0.9569403357,
            -0.2902846773,
            +0.4713967368,
            -0.8819212643,
            +0.7730104534,
            -0.6343932842,
            +0.0980171403,
            -0.9951847267,
            +0.9987954562,
            -0.0490676743,
            +0.6715589548,
            -0.7409511254,
            +0.9039892931,
            -0.4275550934,
            +0.3368898534,
            -0.9415440652,
            +0.9700312532,
            -0.2429801799,
            +0.5141027442,
            -0.8577286100,
            +0.8032075315,
            -0.5956993045,
            +0.1467304745,
            -0.9891765100,
            +0.9891765100,
            -0.1467304745,
            +0.5956993045,
            -0.8032075315,
            +0.8577286100,
            -0.5141027442,
            +0.2429801799,
            -0.9700312532,
            +0.9415440652,
            -0.3368898534,
            +0.4275550934,
            -0.9039892931,
            +0.7409511254,
            -0.6715589548,
            +0.0490676743,
            -0.9987954562,
            +0.9996988187,
            -0.0245412285,
            +0.6895405447,
            -0.7242470830,
            +0.9142097557,
            -0.4052413140,
            +0.3598950365,
            -0.9329927988,
            +0.9757021300,
            -0.2191012402,
            +0.5349976199,
            -0.8448535652,
            +0.8175848132,
            -0.5758081914,
            +0.1709618888,
            -0.9852776424,
            +0.9924795346,
            -0.1224106752,
            +0.6152315906,
            -0.7883464276,
            +0.8700869911,
            -0.4928981922,
            +0.2667127575,
            -0.9637760658,
            +0.9495281806,
            -0.3136817404,
            +0.4496113297,
            -0.8932243012,
            +0.7572088465,
            -0.6531728430,
            +0.0735645636,
            -0.9972904567,
            +0.9972904567,
            -0.0735645636,
            +0.6531728430,
            -0.7572088465,
            +0.8932243012,
            -0.4496113297,
            +0.3136817404,
            -0.9495281806,
            +0.9637760658,
            -0.2667127575,
            +0.4928981922,
            -0.8700869911,
            +0.7883464276,
            -0.6152315906,
            +0.1224106752,
            -0.9924795346,
            +0.9852776424,
            -0.1709618888,
            +0.5758081914,
            -0.8175848132,
            +0.8448535652,
            -0.5349976199,
            +0.2191012402,
            -0.9757021300,
            +0.9329927988,
            -0.3598950365,
            +0.4052413140,
            -0.9142097557,
            +0.7242470830,
            -0.6895405447,
            +0.0245412285,
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            -0.9917097537,
            -0.7921065773,
            -0.6103828063,
            -0.4982276670,
            -0.8670462455,
            -0.9653944417,
            -0.2607941179,
            -0.3195020308,
            -0.9475855910,
            -0.8959662498,
            -0.4441221446,
            -0.6578066933,
            -0.7531867990,
            -0.9977230666,
            -0.0674439196,
            -0.0796824380,
            -0.9968202993,
            -0.7612023855,
            -0.6485144010,
            -0.4550835871,
            -0.8904487232,
            -0.9514350210,
            -0.3078496400,
            -0.2726213554,
            -0.9621214043,
            -0.8730949784,
            -0.4875501601,
            -0.6200572118,
            -0.7845565972,
            -0.9932119492,
            -0.1163186309,
            -0.1770042204,
            -0.9842100924,
            -0.8211025150,
            -0.5707807459,
            -0.5401714727,
            -0.8415549774,
            -0.9770281427,
            -0.2131103199,
            -0.3656129978,
            -0.9307669611,
            -0.9166790599,
            -0.3996241998,
            -0.6939714609,
            -0.7200025080,
            -0.9998305818,
            -0.0184067299,
            -0.0184067299,
            -0.9998305818,
            -0.7200025080,
            -0.6939714609,
            -0.3996241998,
            -0.9166790599,
            -0.9307669611,
            -0.3656129978,
            -0.2131103199,
            -0.9770281427,
            -0.8415549774,
            -0.5401714727,
            -0.5707807459,
            -0.8211025150,
            -0.9842100924,
            -0.1770042204,
            -0.1163186309,
            -0.9932119492,
            -0.7845565972,
            -0.6200572118,
            -0.4875501601,
            -0.8730949784,
            -0.9621214043,
            -0.2726213554,
            -0.3078496400,
            -0.9514350210,
            -0.8904487232,
            -0.4550835871,
            -0.6485144010,
            -0.7612023855,
            -0.9968202993,
            -0.0796824380,
            -0.0674439196,
            -0.9977230666,
            -0.7531867990,
            -0.6578066933,
            -0.4441221446,
            -0.8959662498,
            -0.9475855910,
            -0.3195020308,
            -0.2607941179,
            -0.9653944417,
            -0.8670462455,
            -0.4982276670,
            -0.6103828063,
            -0.7921065773,
            -0.9917097537,
            -0.1284981108,
            -0.1649131205,
            -0.9863080972,
            -0.8140363297,
            -0.5808139581,
            -0.5298036247,
            -0.8481203448,
            -0.9743393828,
            -0.2250839114,
            -0.3541635254,
            -0.9351835099,
            -0.9117060320,
            -0.4108431711,
            -0.6850836678,
            -0.7284643904,
            -0.9995294175,
            -0.0306748032,
            -0.0429382569,
            -0.9990777278,
            -0.7368165689,
            -0.6760927036,
            -0.4220002708,
            -0.9065957045,
            -0.9394592236,
            -0.3426607173,
            -0.2370236060,
            -0.9715038910,
            -0.8545579884,
            -0.5193559902,
            -0.5907597019,
            -0.8068475535,
            -0.9882575677,
            -0.1527971853,
            -0.1406582393,
            -0.9900582103,
            -0.7995372691,
            -0.6006164794,
            -0.5088301425,
            -0.8608669386,
            -0.9685220943,
            -0.2489276057,
            -0.3311063058,
            -0.9435934582,
            -0.9013488470,
            -0.4330938189,
            -0.6669999223,
            -0.7450577854,
            -0.9984755806,
            -0.0551952443,
            -0.0919089565,
            -0.9957674145,
            -0.7691033376,
            -0.6391244449,
            -0.4659764958,
            -0.8847970984,
            -0.9551411683,
            -0.2961508882,
            -0.2844075372,
            -0.9587034749,
            -0.8790122264,
            -0.4767992301,
            -0.6296382389,
            -0.7768884657,
            -0.9945645707,
            -0.1041216339,
            -0.1890686641,
            -0.9819638691,
            -0.8280450453,
            -0.5606615762,
            -0.5504579729,
            -0.8348628750,
            -0.9795697657,
            -0.2011046348,
            -0.3770074102,
            -0.9262102421,
            -0.9215140393,
            -0.3883450467,
            -0.7027547445,
            -0.7114321957,
            -0.9999811753,
            -0.0061358846;
      #endif // FFT_LOW_RAM
   #else // FFT_TWIDDLE_NEED_1024_POINT
   #if defined(FFT_TWIDDLE_NEED_512_POINT)

      .CONST   $fft.NUM_POINTS   512;

      #if FFT_TWIDDLE_PACKED24
         .VAR/DMCONST_WINDOWED16 $fft.twiddle_real[] =
            0x7FFF,  0xFF00,  0x0000,  0x5A82,  0x7AA5,  0x7D86,  0x7641,  0xAFCF,  0x043B,  0x30FB,  0xC589,  0xBE51,
            0x7D8A,  0x5FE7,  0x0748,  0x471C,  0xED95,  0x9267,  0x6A6D,  0x99B8,  0xE313,  0x18F8,  0xB882,  0x75A1,
            0x7F62,  0x37F3,  0x742D,  0x5133,  0xCD9D,  0x0DFE,  0x70E2,  0xCCC3,  0xA946,  0x2528,  0x0C85,  0x82FB,
            0x7A7D,  0x05DA,  0xD7F4,  0x3C56,  0xBA8F,  0x1D34,  0x62F2,  0x02AE,  0xCC33,  0x0C8B,  0xD380,  0x9DC9,
            0x7FD8,  0x88F9,  0xB827,  0x55F5,  0xA5A1,  0x2883,  0x73B5,  0xECC9,  0x45E0,  0x2B1F,  0x3587,  0x7B7C,
            0x7C29,  0xFCE0,  0xE607,  0x41CE,  0x1E92,  0x35F3,  0x66CF,  0x81B3,  0xC020,  0x12C8,  0x1081,  0x62AA,
            0x7E9D,  0x56ED,  0x37F0,  0x4C3F,  0xE099,  0x307F,  0x6DCA,  0x0DBE,  0x31E2,  0x1F19,  0xF983,  0xD604,
            0x7884,  0x84D4,  0xE0CB,  0x36BA,  0x208C,  0x4A14,  0x5ED7,  0x7DAA,  0x0A5B,  0x0647,  0xD980,  0x2778,
            0x7FF6,  0x22FC,  0xDBD5,  0x5842,  0xDDA3,  0x4BDF,  0x7504,  0xD3CC,  0x210D,  0x2E11,  0x0A88,  0x93B1,
            0x7CE3,  0xCFE3,  0xF47E,  0x447A,  0xCD93,  0xDBD7,  0x68A6,  0x9FB6,  0x4BEB,  0x15E2,  0x1481,  0xE26C,
            0x7F09,  0x92F0,  0x54D9,  0x4EBF,  0xE99B,  0x1777,  0x6F5F,  0x03C0,  0xE8B6,  0x2223,  0xA584,  0xA2FC,
            0x798A,  0x24D7,  0xD947,  0x398C,  0xDD8D,  0xAAD3,  0x60EC,  0x38AC,  0x64D5,  0x096A,  0x9080,  0x58C9,
            0x7FA7,  0x37F6,  0x9570,  0x539B,  0x2B9F,  0x13C8,  0x7255,  0x2DC6,  0x7323,  0x2826,  0xB986,  0x75DC,
            0x7B5D,  0x04DD,  0xDC5B,  0x3F17,  0x4A90,  0xA0FD,  0x64E8,  0x89B1,  0x4017,  0x0FAB,  0x2780,  0xF66E,
            0x7E1D,  0x94EA,  0x1DEC,  0x49B4,  0x1597,  0x5961,  0x6C24,  0x29BB,  0x8533,  0x1C0B,  0x8283,  0x1C31,
            0x776C,  0x4FD1,  0xEEF6,  0x33DE,  0xF38A,  0xFB2D,  0x5CB4,  0x21A7,  0xBD23,  0x0324,  0x2B80,  0x09DE,
            0x7FFD,  0x88FE,  0x6DE3,  0x5964,  0x65A4,  0x62EF,  0x75A5,  0x86CD,  0x91AB,  0x2F87,  0x5289,  0x26B6,
            0x7D39,  0x81E5,  0x7D60,  0x45CD,  0x3694,  0xB50E,  0x698C,  0x24B7,  0x961A,  0x176D,  0xDA82,  0x2999,
            0x7F38,  0x58F1,  0xE43D,  0x4FFB,  0x659C,  0x10CD,  0x7023,  0x11C2,  0x47CD,  0x23A6,  0x8885,  0x109D,
            0x7A05,  0xEFD9,  0x57DE,  0x3AF2,  0xEF8E,  0x61D3,  0x61F1,  0x00AD,  0x96EE,  0x0AFB,  0x6880,  0x78D4,
            0x7FC2,  0x56F8,  0x26A4,  0x54CA,  0x0AA0,  0x1C4C,  0x7307,  0xC4C7,  0xDB6C,  0x29A3,  0xC586,  0xF657,
            0x7BC5,  0xE3DF,  0x6090,  0x4073,  0xF291,  0x6956,  0x65DD,  0xFCB2,  0x7E9D,  0x1139,  0xF181,  0x2A1A,
            0x7E5F,  0xE5EB,  0xAA89,  0x4AFB,  0x6D98,  0x42F0,  0x6CF9,  0x35BC,  0xDA3F,  0x1D93,  0x5083,  0x76B4,
            0x77FA,  0xBAD3,  0x6704,  0x354D,  0x908B,  0xA062,  0x5DC7,  0x9DA8,  0xE211,  0x04B6,  0x1980,  0x1634,
            0x7FE9,  0xCCFB,  0x49E7,  0x571D,  0xEFA2,  0x3863,  0x745F,  0x9ECA,  0xB270,  0x2C98,  0xFC88,  0x0546,
            0x7C89,  0x4CE2,  0x6CB0,  0x4325,  0xC193,  0x06CB,  0x67BD,  0x10B5,  0x0493,  0x1455,  0x7781,  0xA01B,
            0x7ED5,  0xE6EE,  0xC60F,  0x4D81,  0x639A,  0x2204,  0x6E96,  0xAABF,  0x8C0E,  0x209F,  0x7084,  0x3A1D,
            0x7909,  0xA9D6,  0x5C3B,  0x3824,  0x948C,  0xF83C,  0x5FE3,  0xB4AB,  0x35F6,  0x07D9,  0x5C80,  0x3DAA,
            0x7F87,  0x2CF5,  0x0498,  0x5269,  0x129E,  0x0F00,  0x719E,  0x2DC5,  0x0D11,  0x26A8,  0x2285,  0xFA11,
            0x7AEF,  0x63DC,  0x5978,  0x3DB8,  0x338F,  0xDCEF,  0x63EF,  0x33B0,  0x049B,  0x0E1B,  0xC380,  0xC7A8,
            0x7DD6,  0x67E8,  0x9226,  0x4869,  0xE696,  0x73DC,  0x6B4A,  0xF2BA,  0x32CA,  0x1A82,  0xA082,  0xC67F,
            0x76D9,  0x4AD0,  0x78AE,  0x326E,  0x558A,  0x5A7A,  0x5B9D,  0x11A6,  0x9B9B,  0x0192,  0x1D80,  0x0278;
      #else
         // twiddle factors needed for <= 512 point fft and ifft routines
         .VAR/DM_REAL_TWIDDLE $fft.twiddle_real[256] =
            +1.0000000000,
            +0.0000000000,
            +0.7071067812,
            -0.7071067812,
            +0.9238795325,
            -0.3826834324,
            +0.3826834324,
            -0.9238795325,
            +0.9807852804,
            -0.1950903220,
            +0.5555702330,
            -0.8314696123,
            +0.8314696123,
            -0.5555702330,
            +0.1950903220,
            -0.9807852804,
            +0.9951847267,
            -0.0980171403,
            +0.6343932842,
            -0.7730104534,
            +0.8819212643,
            -0.4713967368,
            +0.2902846773,
            -0.9569403357,
            +0.9569403357,
            -0.2902846773,
            +0.4713967368,
            -0.8819212643,
            +0.7730104534,
            -0.6343932842,
            +0.0980171403,
            -0.9951847267,
            +0.9987954562,
            -0.0490676743,
            +0.6715589548,
            -0.7409511254,
            +0.9039892931,
            -0.4275550934,
            +0.3368898534,
            -0.9415440652,
            +0.9700312532,
            -0.2429801799,
            +0.5141027442,
            -0.8577286100,
            +0.8032075315,
            -0.5956993045,
            +0.1467304745,
            -0.9891765100,
            +0.9891765100,
            -0.1467304745,
            +0.5956993045,
            -0.8032075315,
            +0.8577286100,
            -0.5141027442,
            +0.2429801799,
            -0.9700312532,
            +0.9415440652,
            -0.3368898534,
            +0.4275550934,
            -0.9039892931,
            +0.7409511254,
            -0.6715589548,
            +0.0490676743,
            -0.9987954562,
            +0.9996988187,
            -0.0245412285,
            +0.6895405447,
            -0.7242470830,
            +0.9142097557,
            -0.4052413140,
            +0.3598950365,
            -0.9329927988,
            +0.9757021300,
            -0.2191012402,
            +0.5349976199,
            -0.8448535652,
            +0.8175848132,
            -0.5758081914,
            +0.1709618888,
            -0.9852776424,
            +0.9924795346,
            -0.1224106752,
            +0.6152315906,
            -0.7883464276,
            +0.8700869911,
            -0.4928981922,
            +0.2667127575,
            -0.9637760658,
            +0.9495281806,
            -0.3136817404,
            +0.4496113297,
            -0.8932243012,
            +0.7572088465,
            -0.6531728430,
            +0.0735645636,
            -0.9972904567,
            +0.9972904567,
            -0.0735645636,
            +0.6531728430,
            -0.7572088465,
            +0.8932243012,
            -0.4496113297,
            +0.3136817404,
            -0.9495281806,
            +0.9637760658,
            -0.2667127575,
            +0.4928981922,
            -0.8700869911,
            +0.7883464276,
            -0.6152315906,
            +0.1224106752,
            -0.9924795346,
            +0.9852776424,
            -0.1709618888,
            +0.5758081914,
            -0.8175848132,
            +0.8448535652,
            -0.5349976199,
            +0.2191012402,
            -0.9757021300,
            +0.9329927988,
            -0.3598950365,
            +0.4052413140,
            -0.9142097557,
            +0.7242470830,
            -0.6895405447,
            +0.0245412285,
            -0.9996988187,
            +0.9999247018,
            -0.0122715383,
            +0.6983762494,
            -0.7157308253,
            +0.9191138517,
            -0.3939920401,
            +0.3713171940,
            -0.9285060805,
            +0.9783173707,
            -0.2071113762,
            +0.5453249884,
            -0.8382247056,
            +0.8245893028,
            -0.5657318108,
            +0.1830398880,
            -0.9831054874,
            +0.9939069700,
            -0.1102222073,
            +0.6248594881,
            -0.7807372286,
            +0.8760700942,
            -0.4821837721,
            +0.2785196894,
            -0.9604305194,
            +0.9533060404,
            -0.3020059493,
            +0.4605387110,
            -0.8876396204,
            +0.7651672656,
            -0.6438315429,
            +0.0857973123,
            -0.9963126122,
            +0.9981181129,
            -0.0613207363,
            +0.6624157776,
            -0.7491363945,
            +0.8986744657,
            -0.4386162385,
            +0.3253102922,
            -0.9456073254,
            +0.9669764710,
            -0.2548656596,
            +0.5035383837,
            -0.8639728561,
            +0.7958369046,
            -0.6055110414,
            +0.1345807085,
            -0.9909026354,
            +0.9873014182,
            -0.1588581433,
            +0.5857978575,
            -0.8104571983,
            +0.8513551931,
            -0.5245896827,
            +0.2310581083,
            -0.9729399522,
            +0.9373390119,
            -0.3484186802,
            +0.4164295601,
            -0.9091679831,
            +0.7326542717,
            -0.6806009978,
            +0.0368072229,
            -0.9993223846,
            +0.9993223846,
            -0.0368072229,
            +0.6806009978,
            -0.7326542717,
            +0.9091679831,
            -0.4164295601,
            +0.3484186802,
            -0.9373390119,
            +0.9729399522,
            -0.2310581083,
            +0.5245896827,
            -0.8513551931,
            +0.8104571983,
            -0.5857978575,
            +0.1588581433,
            -0.9873014182,
            +0.9909026354,
            -0.1345807085,
            +0.6055110414,
            -0.7958369046,
            +0.8639728561,
            -0.5035383837,
            +0.2548656596,
            -0.9669764710,
            +0.9456073254,
            -0.3253102922,
            +0.4386162385,
            -0.8986744657,
            +0.7491363945,
            -0.6624157776,
            +0.0613207363,
            -0.9981181129,
            +0.9963126122,
            -0.0857973123,
            +0.6438315429,
            -0.7651672656,
            +0.8876396204,
            -0.4605387110,
            +0.3020059493,
            -0.9533060404,
            +0.9604305194,
            -0.2785196894,
            +0.4821837721,
            -0.8760700942,
            +0.7807372286,
            -0.6248594881,
            +0.1102222073,
            -0.9939069700,
            +0.9831054874,
            -0.1830398880,
            +0.5657318108,
            -0.8245893028,
            +0.8382247056,
            -0.5453249884,
            +0.2071113762,
            -0.9783173707,
            +0.9285060805,
            -0.3713171940,
            +0.3939920401,
            -0.9191138517,
            +0.7157308253,
            -0.6983762494,
            +0.0122715383,
            -0.9999247018;

         .VAR/DM_IMAG_TWIDDLE $fft.twiddle_imag[256] =
            +0.0000000000,
            -1.0000000000,
            -0.7071067812,
            -0.7071067812,
            -0.3826834324,
            -0.9238795325,
            -0.9238795325,
            -0.3826834324,
            -0.1950903220,
            -0.9807852804,
            -0.8314696123,
            -0.5555702330,
            -0.5555702330,
            -0.8314696123,
            -0.9807852804,
            -0.1950903220,
            -0.0980171403,
            -0.9951847267,
            -0.7730104534,
            -0.6343932842,
            -0.4713967368,
            -0.8819212643,
            -0.9569403357,
            -0.2902846773,
            -0.2902846773,
            -0.9569403357,
            -0.8819212643,
            -0.4713967368,
            -0.6343932842,
            -0.7730104534,
            -0.9951847267,
            -0.0980171403,
            -0.0490676743,
            -0.9987954562,
            -0.7409511254,
            -0.6715589548,
            -0.4275550934,
            -0.9039892931,
            -0.9415440652,
            -0.3368898534,
            -0.2429801799,
            -0.9700312532,
            -0.8577286100,
            -0.5141027442,
            -0.5956993045,
            -0.8032075315,
            -0.9891765100,
            -0.1467304745,
            -0.1467304745,
            -0.9891765100,
            -0.8032075315,
            -0.5956993045,
            -0.5141027442,
            -0.8577286100,
            -0.9700312532,
            -0.2429801799,
            -0.3368898534,
            -0.9415440652,
            -0.9039892931,
            -0.4275550934,
            -0.6715589548,
            -0.7409511254,
            -0.9987954562,
            -0.0490676743,
            -0.0245412285,
            -0.9996988187,
            -0.7242470830,
            -0.6895405447,
            -0.4052413140,
            -0.9142097557,
            -0.9329927988,
            -0.3598950365,
            -0.2191012402,
            -0.9757021300,
            -0.8448535652,
            -0.5349976199,
            -0.5758081914,
            -0.8175848132,
            -0.9852776424,
            -0.1709618888,
            -0.1224106752,
            -0.9924795346,
            -0.7883464276,
            -0.6152315906,
            -0.4928981922,
            -0.8700869911,
            -0.9637760658,
            -0.2667127575,
            -0.3136817404,
            -0.9495281806,
            -0.8932243012,
            -0.4496113297,
            -0.6531728430,
            -0.7572088465,
            -0.9972904567,
            -0.0735645636,
            -0.0735645636,
            -0.9972904567,
            -0.7572088465,
            -0.6531728430,
            -0.4496113297,
            -0.8932243012,
            -0.9495281806,
            -0.3136817404,
            -0.2667127575,
            -0.9637760658,
            -0.8700869911,
            -0.4928981922,
            -0.6152315906,
            -0.7883464276,
            -0.9924795346,
            -0.1224106752,
            -0.1709618888,
            -0.9852776424,
            -0.8175848132,
            -0.5758081914,
            -0.5349976199,
            -0.8448535652,
            -0.9757021300,
            -0.2191012402,
            -0.3598950365,
            -0.9329927988,
            -0.9142097557,
            -0.4052413140,
            -0.6895405447,
            -0.7242470830,
            -0.9996988187,
            -0.0245412285,
            -0.0122715383,
            -0.9999247018,
            -0.7157308253,
            -0.6983762494,
            -0.3939920401,
            -0.9191138517,
            -0.9285060805,
            -0.3713171940,
            -0.2071113762,
            -0.9783173707,
            -0.8382247056,
            -0.5453249884,
            -0.5657318108,
            -0.8245893028,
            -0.9831054874,
            -0.1830398880,
            -0.1102222073,
            -0.9939069700,
            -0.7807372286,
            -0.6248594881,
            -0.4821837721,
            -0.8760700942,
            -0.9604305194,
            -0.2785196894,
            -0.3020059493,
            -0.9533060404,
            -0.8876396204,
            -0.4605387110,
            -0.6438315429,
            -0.7651672656,
            -0.9963126122,
            -0.0857973123,
            -0.0613207363,
            -0.9981181129,
            -0.7491363945,
            -0.6624157776,
            -0.4386162385,
            -0.8986744657,
            -0.9456073254,
            -0.3253102922,
            -0.2548656596,
            -0.9669764710,
            -0.8639728561,
            -0.5035383837,
            -0.6055110414,
            -0.7958369046,
            -0.9909026354,
            -0.1345807085,
            -0.1588581433,
            -0.9873014182,
            -0.8104571983,
            -0.5857978575,
            -0.5245896827,
            -0.8513551931,
            -0.9729399522,
            -0.2310581083,
            -0.3484186802,
            -0.9373390119,
            -0.9091679831,
            -0.4164295601,
            -0.6806009978,
            -0.7326542717,
            -0.9993223846,
            -0.0368072229,
            -0.0368072229,
            -0.9993223846,
            -0.7326542717,
            -0.6806009978,
            -0.4164295601,
            -0.9091679831,
            -0.9373390119,
            -0.3484186802,
            -0.2310581083,
            -0.9729399522,
            -0.8513551931,
            -0.5245896827,
            -0.5857978575,
            -0.8104571983,
            -0.9873014182,
            -0.1588581433,
            -0.1345807085,
            -0.9909026354,
            -0.7958369046,
            -0.6055110414,
            -0.5035383837,
            -0.8639728561,
            -0.9669764710,
            -0.2548656596,
            -0.3253102922,
            -0.9456073254,
            -0.8986744657,
            -0.4386162385,
            -0.6624157776,
            -0.7491363945,
            -0.9981181129,
            -0.0613207363,
            -0.0857973123,
            -0.9963126122,
            -0.7651672656,
            -0.6438315429,
            -0.4605387110,
            -0.8876396204,
            -0.9533060404,
            -0.3020059493,
            -0.2785196894,
            -0.9604305194,
            -0.8760700942,
            -0.4821837721,
            -0.6248594881,
            -0.7807372286,
            -0.9939069700,
            -0.1102222073,
            -0.1830398880,
            -0.9831054874,
            -0.8245893028,
            -0.5657318108,
            -0.5453249884,
            -0.8382247056,
            -0.9783173707,
            -0.2071113762,
            -0.3713171940,
            -0.9285060805,
            -0.9191138517,
            -0.3939920401,
            -0.6983762494,
            -0.7157308253,
            -0.9999247018,
            -0.0122715383;
      #endif // FFT_LOW_RAM
   #else // FFT_TWIDDLE_NEED_512_POINT
   #if defined(FFT_TWIDDLE_NEED_256_POINT)

      .CONST   $fft.NUM_POINTS   256;

      #if FFT_TWIDDLE_PACKED24
         .VAR/DMCONST_WINDOWED16 $fft.twiddle_real[] =
            0x7FFF,  0xFF00,  0x0000,  0x5A82,  0x7AA5,  0x7D86,  0x7641,  0xAFCF,  0x043B,  0x30FB,  0xC589,  0xBE51,
            0x7D8A,  0x5FE7,  0x0748,  0x471C,  0xED95,  0x9267,  0x6A6D,  0x99B8,  0xE313,  0x18F8,  0xB882,  0x75A1,
            0x7F62,  0x37F3,  0x742D,  0x5133,  0xCD9D,  0x0DFE,  0x70E2,  0xCCC3,  0xA946,  0x2528,  0x0C85,  0x82FB,
            0x7A7D,  0x05DA,  0xD7F4,  0x3C56,  0xBA8F,  0x1D34,  0x62F2,  0x02AE,  0xCC33,  0x0C8B,  0xD380,  0x9DC9,
            0x7FD8,  0x88F9,  0xB827,  0x55F5,  0xA5A1,  0x2883,  0x73B5,  0xECC9,  0x45E0,  0x2B1F,  0x3587,  0x7B7C,
            0x7C29,  0xFCE0,  0xE607,  0x41CE,  0x1E92,  0x35F3,  0x66CF,  0x81B3,  0xC020,  0x12C8,  0x1081,  0x62AA,
            0x7E9D,  0x56ED,  0x37F0,  0x4C3F,  0xE099,  0x307F,  0x6DCA,  0x0DBE,  0x31E2,  0x1F19,  0xF983,  0xD604,
            0x7884,  0x84D4,  0xE0CB,  0x36BA,  0x208C,  0x4A14,  0x5ED7,  0x7DAA,  0x0A5B,  0x0647,  0xD980,  0x2778,
            0x7FF6,  0x22FC,  0xDBD5,  0x5842,  0xDDA3,  0x4BDF,  0x7504,  0xD3CC,  0x210D,  0x2E11,  0x0A88,  0x93B1,
            0x7CE3,  0xCFE3,  0xF47E,  0x447A,  0xCD93,  0xDBD7,  0x68A6,  0x9FB6,  0x4BEB,  0x15E2,  0x1481,  0xE26C,
            0x7F09,  0x92F0,  0x54D9,  0x4EBF,  0xE99B,  0x1777,  0x6F5F,  0x03C0,  0xE8B6,  0x2223,  0xA584,  0xA2FC,
            0x798A,  0x24D7,  0xD947,  0x398C,  0xDD8D,  0xAAD3,  0x60EC,  0x38AC,  0x64D5,  0x096A,  0x9080,  0x58C9,
            0x7FA7,  0x37F6,  0x9570,  0x539B,  0x2B9F,  0x13C8,  0x7255,  0x2DC6,  0x7323,  0x2826,  0xB986,  0x75DC,
            0x7B5D,  0x04DD,  0xDC5B,  0x3F17,  0x4A90,  0xA0FD,  0x64E8,  0x89B1,  0x4017,  0x0FAB,  0x2780,  0xF66E,
            0x7E1D,  0x94EA,  0x1DEC,  0x49B4,  0x1597,  0x5961,  0x6C24,  0x29BB,  0x8533,  0x1C0B,  0x8283,  0x1C31,
            0x776C,  0x4FD1,  0xEEF6,  0x33DE,  0xF38A,  0xFB2D,  0x5CB4,  0x21A7,  0xBD23,  0x0324,  0x2B80,  0x09DE;
      #else
         // twiddle factors needed for <= 256 point fft and ifft routines
         .VAR/DM_REAL_TWIDDLE $fft.twiddle_real[128] =
            +1.0000000000,
            +0.0000000000,
            +0.7071067812,
            -0.7071067812,
            +0.9238795325,
            -0.3826834324,
            +0.3826834324,
            -0.9238795325,
            +0.9807852804,
            -0.1950903220,
            +0.5555702330,
            -0.8314696123,
            +0.8314696123,
            -0.5555702330,
            +0.1950903220,
            -0.9807852804,
            +0.9951847267,
            -0.0980171403,
            +0.6343932842,
            -0.7730104534,
            +0.8819212643,
            -0.4713967368,
            +0.2902846773,
            -0.9569403357,
            +0.9569403357,
            -0.2902846773,
            +0.4713967368,
            -0.8819212643,
            +0.7730104534,
            -0.6343932842,
            +0.0980171403,
            -0.9951847267,
            +0.9987954562,
            -0.0490676743,
            +0.6715589548,
            -0.7409511254,
            +0.9039892931,
            -0.4275550934,
            +0.3368898534,
            -0.9415440652,
            +0.9700312532,
            -0.2429801799,
            +0.5141027442,
            -0.8577286100,
            +0.8032075315,
            -0.5956993045,
            +0.1467304745,
            -0.9891765100,
            +0.9891765100,
            -0.1467304745,
            +0.5956993045,
            -0.8032075315,
            +0.8577286100,
            -0.5141027442,
            +0.2429801799,
            -0.9700312532,
            +0.9415440652,
            -0.3368898534,
            +0.4275550934,
            -0.9039892931,
            +0.7409511254,
            -0.6715589548,
            +0.0490676743,
            -0.9987954562,
            +0.9996988187,
            -0.0245412285,
            +0.6895405447,
            -0.7242470830,
            +0.9142097557,
            -0.4052413140,
            +0.3598950365,
            -0.9329927988,
            +0.9757021300,
            -0.2191012402,
            +0.5349976199,
            -0.8448535652,
            +0.8175848132,
            -0.5758081914,
            +0.1709618888,
            -0.9852776424,
            +0.9924795346,
            -0.1224106752,
            +0.6152315906,
            -0.7883464276,
            +0.8700869911,
            -0.4928981922,
            +0.2667127575,
            -0.9637760658,
            +0.9495281806,
            -0.3136817404,
            +0.4496113297,
            -0.8932243012,
            +0.7572088465,
            -0.6531728430,
            +0.0735645636,
            -0.9972904567,
            +0.9972904567,
            -0.0735645636,
            +0.6531728430,
            -0.7572088465,
            +0.8932243012,
            -0.4496113297,
            +0.3136817404,
            -0.9495281806,
            +0.9637760658,
            -0.2667127575,
            +0.4928981922,
            -0.8700869911,
            +0.7883464276,
            -0.6152315906,
            +0.1224106752,
            -0.9924795346,
            +0.9852776424,
            -0.1709618888,
            +0.5758081914,
            -0.8175848132,
            +0.8448535652,
            -0.5349976199,
            +0.2191012402,
            -0.9757021300,
            +0.9329927988,
            -0.3598950365,
            +0.4052413140,
            -0.9142097557,
            +0.7242470830,
            -0.6895405447,
            +0.0245412285,
            -0.9996988187;

         .VAR/DM_IMAG_TWIDDLE $fft.twiddle_imag[128] =
            +0.0000000000,
            -1.0000000000,
            -0.7071067812,
            -0.7071067812,
            -0.3826834324,
            -0.9238795325,
            -0.9238795325,
            -0.3826834324,
            -0.1950903220,
            -0.9807852804,
            -0.8314696123,
            -0.5555702330,
            -0.5555702330,
            -0.8314696123,
            -0.9807852804,
            -0.1950903220,
            -0.0980171403,
            -0.9951847267,
            -0.7730104534,
            -0.6343932842,
            -0.4713967368,
            -0.8819212643,
            -0.9569403357,
            -0.2902846773,
            -0.2902846773,
            -0.9569403357,
            -0.8819212643,
            -0.4713967368,
            -0.6343932842,
            -0.7730104534,
            -0.9951847267,
            -0.0980171403,
            -0.0490676743,
            -0.9987954562,
            -0.7409511254,
            -0.6715589548,
            -0.4275550934,
            -0.9039892931,
            -0.9415440652,
            -0.3368898534,
            -0.2429801799,
            -0.9700312532,
            -0.8577286100,
            -0.5141027442,
            -0.5956993045,
            -0.8032075315,
            -0.9891765100,
            -0.1467304745,
            -0.1467304745,
            -0.9891765100,
            -0.8032075315,
            -0.5956993045,
            -0.5141027442,
            -0.8577286100,
            -0.9700312532,
            -0.2429801799,
            -0.3368898534,
            -0.9415440652,
            -0.9039892931,
            -0.4275550934,
            -0.6715589548,
            -0.7409511254,
            -0.9987954562,
            -0.0490676743,
            -0.0245412285,
            -0.9996988187,
            -0.7242470830,
            -0.6895405447,
            -0.4052413140,
            -0.9142097557,
            -0.9329927988,
            -0.3598950365,
            -0.2191012402,
            -0.9757021300,
            -0.8448535652,
            -0.5349976199,
            -0.5758081914,
            -0.8175848132,
            -0.9852776424,
            -0.1709618888,
            -0.1224106752,
            -0.9924795346,
            -0.7883464276,
            -0.6152315906,
            -0.4928981922,
            -0.8700869911,
            -0.9637760658,
            -0.2667127575,
            -0.3136817404,
            -0.9495281806,
            -0.8932243012,
            -0.4496113297,
            -0.6531728430,
            -0.7572088465,
            -0.9972904567,
            -0.0735645636,
            -0.0735645636,
            -0.9972904567,
            -0.7572088465,
            -0.6531728430,
            -0.4496113297,
            -0.8932243012,
            -0.9495281806,
            -0.3136817404,
            -0.2667127575,
            -0.9637760658,
            -0.8700869911,
            -0.4928981922,
            -0.6152315906,
            -0.7883464276,
            -0.9924795346,
            -0.1224106752,
            -0.1709618888,
            -0.9852776424,
            -0.8175848132,
            -0.5758081914,
            -0.5349976199,
            -0.8448535652,
            -0.9757021300,
            -0.2191012402,
            -0.3598950365,
            -0.9329927988,
            -0.9142097557,
            -0.4052413140,
            -0.6895405447,
            -0.7242470830,
            -0.9996988187,
            -0.0245412285;
      #endif // FFT_LOW_RAM
   #else // FFT_TWIDDLE_NEED_256_POINT
   #if defined(FFT_TWIDDLE_NEED_128_POINT)

      .CONST   $fft.NUM_POINTS   128;

      #if FFT_TWIDDLE_PACKED24
         .VAR/DMCONST_WINDOWED16 $fft.twiddle_real[] =
            0x7FFF,  0xFF00,  0x0000,  0x5A82,  0x7AA5,  0x7D86,  0x7641,  0xAFCF,  0x043B,  0x30FB,  0xC589,  0xBE51,
            0x7D8A,  0x5FE7,  0x0748,  0x471C,  0xED95,  0x9267,  0x6A6D,  0x99B8,  0xE313,  0x18F8,  0xB882,  0x75A1,
            0x7F62,  0x37F3,  0x742D,  0x5133,  0xCD9D,  0x0DFE,  0x70E2,  0xCCC3,  0xA946,  0x2528,  0x0C85,  0x82FB,
            0x7A7D,  0x05DA,  0xD7F4,  0x3C56,  0xBA8F,  0x1D34,  0x62F2,  0x02AE,  0xCC33,  0x0C8B,  0xD380,  0x9DC9,
            0x7FD8,  0x88F9,  0xB827,  0x55F5,  0xA5A1,  0x2883,  0x73B5,  0xECC9,  0x45E0,  0x2B1F,  0x3587,  0x7B7C,
            0x7C29,  0xFCE0,  0xE607,  0x41CE,  0x1E92,  0x35F3,  0x66CF,  0x81B3,  0xC020,  0x12C8,  0x1081,  0x62AA,
            0x7E9D,  0x56ED,  0x37F0,  0x4C3F,  0xE099,  0x307F,  0x6DCA,  0x0DBE,  0x31E2,  0x1F19,  0xF983,  0xD604,
            0x7884,  0x84D4,  0xE0CB,  0x36BA,  0x208C,  0x4A14,  0x5ED7,  0x7DAA,  0x0A5B,  0x0647,  0xD980,  0x2778;
      #else
         // twiddle factors needed for <= 128 point fft and ifft routines
         .VAR/DM_REAL_TWIDDLE $fft.twiddle_real[64] =
            +1.0000000000,
            +0.0000000000,
            +0.7071067812,
            -0.7071067812,
            +0.9238795325,
            -0.3826834324,
            +0.3826834324,
            -0.9238795325,
            +0.9807852804,
            -0.1950903220,
            +0.5555702330,
            -0.8314696123,
            +0.8314696123,
            -0.5555702330,
            +0.1950903220,
            -0.9807852804,
            +0.9951847267,
            -0.0980171403,
            +0.6343932842,
            -0.7730104534,
            +0.8819212643,
            -0.4713967368,
            +0.2902846773,
            -0.9569403357,
            +0.9569403357,
            -0.2902846773,
            +0.4713967368,
            -0.8819212643,
            +0.7730104534,
            -0.6343932842,
            +0.0980171403,
            -0.9951847267,
            +0.9987954562,
            -0.0490676743,
            +0.6715589548,
            -0.7409511254,
            +0.9039892931,
            -0.4275550934,
            +0.3368898534,
            -0.9415440652,
            +0.9700312532,
            -0.2429801799,
            +0.5141027442,
            -0.8577286100,
            +0.8032075315,
            -0.5956993045,
            +0.1467304745,
            -0.9891765100,
            +0.9891765100,
            -0.1467304745,
            +0.5956993045,
            -0.8032075315,
            +0.8577286100,
            -0.5141027442,
            +0.2429801799,
            -0.9700312532,
            +0.9415440652,
            -0.3368898534,
            +0.4275550934,
            -0.9039892931,
            +0.7409511254,
            -0.6715589548,
            +0.0490676743,
            -0.9987954562;

         .VAR/DM_IMAG_TWIDDLE $fft.twiddle_imag[64] =
            +0.0000000000,
            -1.0000000000,
            -0.7071067812,
            -0.7071067812,
            -0.3826834324,
            -0.9238795325,
            -0.9238795325,
            -0.3826834324,
            -0.1950903220,
            -0.9807852804,
            -0.8314696123,
            -0.5555702330,
            -0.5555702330,
            -0.8314696123,
            -0.9807852804,
            -0.1950903220,
            -0.0980171403,
            -0.9951847267,
            -0.7730104534,
            -0.6343932842,
            -0.4713967368,
            -0.8819212643,
            -0.9569403357,
            -0.2902846773,
            -0.2902846773,
            -0.9569403357,
            -0.8819212643,
            -0.4713967368,
            -0.6343932842,
            -0.7730104534,
            -0.9951847267,
            -0.0980171403,
            -0.0490676743,
            -0.9987954562,
            -0.7409511254,
            -0.6715589548,
            -0.4275550934,
            -0.9039892931,
            -0.9415440652,
            -0.3368898534,
            -0.2429801799,
            -0.9700312532,
            -0.8577286100,
            -0.5141027442,
            -0.5956993045,
            -0.8032075315,
            -0.9891765100,
            -0.1467304745,
            -0.1467304745,
            -0.9891765100,
            -0.8032075315,
            -0.5956993045,
            -0.5141027442,
            -0.8577286100,
            -0.9700312532,
            -0.2429801799,
            -0.3368898534,
            -0.9415440652,
            -0.9039892931,
            -0.4275550934,
            -0.6715589548,
            -0.7409511254,
            -0.9987954562,
            -0.0490676743;
      #endif // FFT_LOW_RAM
   #else // FFT_TWIDDLE_NEED_128_POINT
   #if defined(FFT_TWIDDLE_NEED_64_POINT)

      .CONST   $fft.NUM_POINTS   64;

      #if FFT_TWIDDLE_PACKED24
         .VAR/DMCONST_WINDOWED16 $fft.twiddle_real[] =
            0x7FFF,  0xFF00,  0x0000,  0x5A82,  0x7AA5,  0x7D86,  0x7641,  0xAFCF,  0x043B,  0x30FB,  0xC589,  0xBE51,
            0x7D8A,  0x5FE7,  0x0748,  0x471C,  0xED95,  0x9267,  0x6A6D,  0x99B8,  0xE313,  0x18F8,  0xB882,  0x75A1,
            0x7F62,  0x37F3,  0x742D,  0x5133,  0xCD9D,  0x0DFE,  0x70E2,  0xCCC3,  0xA946,  0x2528,  0x0C85,  0x82FB,
            0x7A7D,  0x05DA,  0xD7F4,  0x3C56,  0xBA8F,  0x1D34,  0x62F2,  0x02AE,  0xCC33,  0x0C8B,  0xD380,  0x9DC9;
      #else
         // twiddle factors needed for <= 64 point fft and ifft routines
         .VAR/DM_REAL_TWIDDLE $fft.twiddle_real[32] =
            +1.0000000000,
            +0.0000000000,
            +0.7071067812,
            -0.7071067812,
            +0.9238795325,
            -0.3826834324,
            +0.3826834324,
            -0.9238795325,
            +0.9807852804,
            -0.1950903220,
            +0.5555702330,
            -0.8314696123,
            +0.8314696123,
            -0.5555702330,
            +0.1950903220,
            -0.9807852804,
            +0.9951847267,
            -0.0980171403,
            +0.6343932842,
            -0.7730104534,
            +0.8819212643,
            -0.4713967368,
            +0.2902846773,
            -0.9569403357,
            +0.9569403357,
            -0.2902846773,
            +0.4713967368,
            -0.8819212643,
            +0.7730104534,
            -0.6343932842,
            +0.0980171403,
            -0.9951847267;

         .VAR/DM_IMAG_TWIDDLE $fft.twiddle_imag[32] =
            +0.0000000000,
            -1.0000000000,
            -0.7071067812,
            -0.7071067812,
            -0.3826834324,
            -0.9238795325,
            -0.9238795325,
            -0.3826834324,
            -0.1950903220,
            -0.9807852804,
            -0.8314696123,
            -0.5555702330,
            -0.5555702330,
            -0.8314696123,
            -0.9807852804,
            -0.1950903220,
            -0.0980171403,
            -0.9951847267,
            -0.7730104534,
            -0.6343932842,
            -0.4713967368,
            -0.8819212643,
            -0.9569403357,
            -0.2902846773,
            -0.2902846773,
            -0.9569403357,
            -0.8819212643,
            -0.4713967368,
            -0.6343932842,
            -0.7730104534,
            -0.9951847267,
            -0.0980171403;
      #endif // FFT_LOW_RAM
   #else // FFT_TWIDDLE_NEED_64_POINT
   #if defined(FFT_TWIDDLE_NEED_32_POINT)

      .CONST   $fft.NUM_POINTS   32;

      #if FFT_TWIDDLE_PACKED24
         .VAR/DMCONST_WINDOWED16 $fft.twiddle_real[] =
            0x7FFF,  0xFF00,  0x0000,  0x5A82,  0x7AA5,  0x7D86,  0x7641,  0xAFCF,  0x043B,  0x30FB,  0xC589,  0xBE51,
            0x7D8A,  0x5FE7,  0x0748,  0x471C,  0xED95,  0x9267,  0x6A6D,  0x99B8,  0xE313,  0x18F8,  0xB882,  0x75A1;
      #else
         // twiddle factors needed for <= 32 point fft and ifft routines
         .VAR/DM_REAL_TWIDDLE $fft.twiddle_real[16] =
            +1.0000000000,
            +0.0000000000,
            +0.7071067812,
            -0.7071067812,
            +0.9238795325,
            -0.3826834324,
            +0.3826834324,
            -0.9238795325,
            +0.9807852804,
            -0.1950903220,
            +0.5555702330,
            -0.8314696123,
            +0.8314696123,
            -0.5555702330,
            +0.1950903220,
            -0.9807852804;

         .VAR/DM_IMAG_TWIDDLE $fft.twiddle_imag[16] =
            +0.0000000000,
            -1.0000000000,
            -0.7071067812,
            -0.7071067812,
            -0.3826834324,
            -0.9238795325,
            -0.9238795325,
            -0.3826834324,
            -0.1950903220,
            -0.9807852804,
            -0.8314696123,
            -0.5555702330,
            -0.5555702330,
            -0.8314696123,
            -0.9807852804,
            -0.1950903220;
      #endif
   #else // FFT_TWIDDLE_NEED_32_POINT
   #if defined(FFT_TWIDDLE_NEED_16_POINT)

      .CONST   $fft.NUM_POINTS   16;

      #if FFT_TWIDDLE_PACKED24
         .VAR/DMCONST_WINDOWED16 $fft.twiddle_real[] =
            0x7FFF,  0xFF00,  0x0000,  0x5A82,  0x7AA5,  0x7D86,  0x7641,  0xAFCF,  0x043B,  0x30FB,  0xC589,  0xBE51;
      #else
          // twiddle factors needed for <= 16 point fft and ifft routines
         .VAR/DM_REAL_TWIDDLE $fft.twiddle_real[8] =
            +1.0000000000,
            +0.0000000000,
            +0.7071067812,
            -0.7071067812,
            +0.9238795325,
            -0.3826834324,
            +0.3826834324,
            -0.9238795325;

         .VAR/DM_IMAG_TWIDDLE $fft.twiddle_imag[8] =
            +0.0000000000,
            -1.0000000000,
            -0.7071067812,
            -0.7071067812,
            -0.3826834324,
            -0.9238795325,
            -0.9238795325,
            -0.3826834324;
      #endif // FFT_LOW_RAM
   #else // FFT_TWIDDLE_NEED_16_POINT
   #if defined(FFT_TWIDDLE_NEED_8_POINT)

      .CONST   $fft.NUM_POINTS   8;

      #if FFT_TWIDDLE_PACKED24
         .VAR/DMCONST_WINDOWED16 $fft.twiddle_real[] =
            0x7FFF,  0xFF00,  0x0000,  0x5A82,  0x7AA5,  0x7D86;
      #else
          // twiddle factors needed for <= 8 point fft and ifft routines
         .VAR/DM_REAL_TWIDDLE $fft.twiddle_real[4] =
            +1.0000000000,
            +0.0000000000,
            +0.7071067812,
            -0.7071067812;

         .VAR/DM_IMAG_TWIDDLE $fft.twiddle_imag[4] =
            +0.0000000000,
            -1.0000000000,
            -0.7071067812,
            -0.7071067812;
      #endif // FFT_LOW_RAM
   #else // FFT_TWIDDLE_NEED_8_POINT

      // if FFT_TWIDDLE_NEED_xxx_POINT is not defined then we don't define any twiddle factors

   #endif // FFT_TWIDDLE_NEED_8_POINT
   #endif // FFT_TWIDDLE_NEED_16_POINT
   #endif // FFT_TWIDDLE_NEED_32_POINT
   #endif // FFT_TWIDDLE_NEED_64_POINT
   #endif // FFT_TWIDDLE_NEED_128_POINT
   #endif // FFT_TWIDDLE_NEED_256_POINT
   #endif // FFT_TWIDDLE_NEED_512_POINT
   #endif // FFT_TWIDDLE_NEED_1024_POINT
   #endif // FFT_TWIDDLE_NEED_2048_POINT

.ENDMODULE;

#endif // FFT_TWIDDLE_INCLUDED
